Answer:
10.7 ft²
Step-by-step explanation:
The most important formula you'll need to solve this is [tex]\frac{1}{2}[/tex]*b*h which is the formula for solving the area of a 2 dimensional triangle.
Finding the base:
The base of the 2-dimensional base is 2
The height of the 2-dimensional base is 1.7
Using [tex]\frac{1}{2}[/tex]*b*h, we get [tex]\frac{1}{2}[/tex]*2*1.7 which equals 1.7
The area of the 2 dimensional base is 1.7
Finding the lateral faces:
The lateral faces are all the same sizes so we'll just find the area of 1 and multiply it by 3.
The base of a lateral face is 2
The height of a lateral face is 3
Using [tex]\frac{1}{2}[/tex]*b*h, we get [tex]\frac{1}{2}[/tex]*2*3 which equals 3
The area of a lateral face is 3
Since there are 3 lateral faces, we multiply the area of one lateral face by 3 or 3*3 which equals 9
The area of all the lateral faces are 9
Since we need to find the total surface area, we add the area of the base and all the lateral faces. So:
9+1.7=10.7
The surface area of this triangular pyramid is 10.7 ft²
